Dveco.jl

### A Pluto.jl notebook ###
# v0.18.0

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
        el
    end
end

# ╔═╡ 4478d0a8-360a-4792-8859-244d80d2902b
using Colors, FileIO, ImageIO, ImageShow, QuartzImageIO

# ╔═╡ 0e4ef764-37f3-4db8-b7d5-2d40d81e2797
using Statistics

# ╔═╡ 1750a808-0c77-466c-a7e8-e569082c60af
using PlutoUI

# ╔═╡ a3966b72-930d-4485-94f7-177c3c5a7391
using Plots

# ╔═╡ c4c0dd00-655c-419a-9b8d-3afb78f139b1
using LsqFit

# ╔═╡ 670a7c9a-7dd9-11ec-2f9e-5daa27e49f3c
md"""
# Dveco, non-jpeg image compression
For Pablo
"""

# ╔═╡ 8e642f27-ea51-4cf1-b798-d8a586770b57
md"""
## Libraries and stuff to get up and running
"""

# ╔═╡ c6e8d6fb-7993-4d9e-bf0a-c4dc1d1e4b4a
PlutoUI.TableOfContents()

# ╔═╡ 419dfb6d-f7ca-46eb-984a-99d10b804e89
Image = Matrix{<:Color}

# ╔═╡ b389b734-e61a-4348-9720-3475b654ad8d
Channel = Matrix{<:Number}

# ╔═╡ 386615cc-6bd9-4a49-ba70-39f277c0e1db
struct FancyPixel
	value::Number
	size::Tuple{Int64, Int64}
end

# ╔═╡ 6b6bb9b9-b2c1-409e-9fc1-60285c1d2177
function luminance(pixel::Color)
	0.2126*pixel.r + 0.7152*pixel.g + 0.0722*pixel.b
end

# ╔═╡ 85f6c36d-a395-442f-8ba7-f2a8506d1544
luminance(image::Image) = luminance.(image)

# ╔═╡ 394fb978-f350-4ddc-9de5-d5114e9a87ed
md"""
## Main implementation
"""

# ╔═╡ 4377d345-71b9-4aff-b8d9-a45c4e9eb05e
md"""
### Compression
"""

# ╔═╡ 9bbc975a-d0d8-4f8e-b6b6-85fc2a9823ca
md"""
First, we make a function to mortar a matrix (divide in 4)
"""

# ╔═╡ b68f03ea-e884-4614-b1ff-c1d92118c30b
function mortar(matrix::Matrix{T})::Matrix{Matrix{T}} where {T}
	(fx, fy) = size(matrix)

	x = fx÷2
	y = fy÷2

	brick = [
		[matrix[1:x, 1:y]] [matrix[1:x, y+1:end]]
		[matrix[x+1:end, 1:y]] [matrix[x+1:end, y+1:end]]
	]

	brick
end

# ╔═╡ b4ad67b5-5b71-444b-ad68-5064587905d4
md"""
Then, we make a recursive compression algorithm that takes the average if the standard deviation of a region is above a certain threshold
"""

# ╔═╡ d5623e00-571f-407f-a88c-f1a020102e1d
function compress(channel::Channel, threashold::Number)
	dev = length(channel) == 1 ? 0 : std(channel)

	if dev > threashold		
		compress.(mortar(channel), threashold)
	else
		s = size(channel)
		if s == (1, 1)
			channel[1, 1]
		else
			FancyPixel(mean(channel), s)
		end
	end
end

# ╔═╡ dccb5b97-4865-436a-b2cb-e774b2b1d79b
md"""
### Decompression
"""

# ╔═╡ daf3699e-267c-4b65-a39a-af0c1978430c
md"""
To decompress the image we need to repeat the value stored
"""

# ╔═╡ 280de3c0-6329-4a74-b684-3adebefe033e
function reconstruct(pixel::Real)
	pixel
end

# ╔═╡ 7bcb0d03-a859-496f-b5f4-4d6ba17ab07a
function reconstruct(pixel::FancyPixel)
	fill(pixel.value, pixel.size)
end

# ╔═╡ 5e91243f-8f61-4076-a1bc-b60b5ce8fb4c
md"""
And then we need to flatten the mortified (xd) matrix
"""

# ╔═╡ 2fe9e1dc-81ab-450c-9544-6429c2a80d6b
function flatten(matrix::Matrix{<:Any})
	caca = nothing
	for i in 1:size(matrix)[1]
		caca = matrix[i, :]
	end
	caca

	vcat([
		hcat(matrix[i, :]...) for i in 1:size(matrix)[1]
	]...)
end

# ╔═╡ 83769dd6-6b73-4821-b87d-f9b3ae12efe6
function reconstruct(compressed::Array{<:Any})
	compressed = map(reconstruct, compressed)
	flatten(compressed)
end

# ╔═╡ c7cbae3a-248e-4f9a-ba42-b2c94a570665
md"""
### Demo
"""

# ╔═╡ 98eb608b-c7f1-45a0-911c-4d5ef1a1fdc5
function show_compressed(channel::Channel, threshold::Number)
	RGB.(reconstruct(compress(channel, threshold)))
end

# ╔═╡ 347f8c01-96d6-41d0-a785-15e51886f89d
begin
	url = "https://upload.wikimedia.org/wikipedia/commons/3/39/GodfreyKneller-IsaacNewton-1689.jpg" 
	philip_filename = download(url)
	test = load(philip_filename)
end

# ╔═╡ c32aeff2-72d4-4869-aaa7-e9bb26d59ab8
@bind threshold_bnw Slider(0.3:-0.001:0)

# ╔═╡ 751e0e94-7899-4c25-8519-6ce98b7b5f24
md"""
## Adding color

Kinda rudimentary
"""

# ╔═╡ cf2d80f0-9b2a-4162-a1b5-acc41a3dedcc
function channels(image::Image)
	[red.(image), green.(image), blue.(image)]
end

# ╔═╡ 0320566c-c8ca-4696-9aff-4d737be2ea97
function compress_by_channel(image::Image, threshold::Number)
	compress.(channels(image), threshold)
end

# ╔═╡ 8802eb09-e619-4d04-ae11-37fb19649fa1
function show_compressed(image::Image, threshold::Number)
	comp = compress_by_channel(image, threshold)
	comp = reconstruct.(comp)
	[RGB(r, g, b) for (r, g, b) in zip(comp...)]
end

# ╔═╡ 7cfd7bc3-fcd6-4034-9d8d-36a87eac1627
show_compressed(luminance(test), threshold_bnw)

# ╔═╡ c4d5c2f5-6603-4309-8fbf-ed41a8e90675
md"""
## File size

Rudimentary. 
"""

# ╔═╡ e0452dc4-8bd1-470a-9cfd-782dfc4e301e
function filesize(pixel::Real, size_per_pixel = 3)
	return 1
end

# ╔═╡ 4d7c4da8-58aa-42af-a8a1-89160e73e08f
function filesize(compressed::Matrix, size_per_pixel = 3)
	tally = 0
	for i in compressed
		tally += filesize(i, size_per_pixel)
	end
	tally
end

# ╔═╡ 414a7f26-6c02-4deb-888f-62acbf52238c
function filesize(pixel::FancyPixel, size_per_pixel = 3)
	size_per_pixel
end

# ╔═╡ bf58ce82-c5ec-416b-8d42-d5673c2d156d
filesize(compress(luminance(test), 0.01))

# ╔═╡ 3ce732b7-d7fd-434b-95f9-f37c33192934
function compression_quality(original::Channel, compressed::Channel)
	sum([abs(o - c) for (o, c) in zip(original, compressed)])
end

# ╔═╡ 2db8f5bc-0b2a-4a1e-9cdb-125af1b001c4
function compression_stats(image::Image, threshold::Number)
	s = size(image)
	original = s[1] * s[2] * 3
	compressed = compress_by_channel(image, threshold)
	reconstructed = [RGB(r,g,b) for (r,g,b) in zip(reconstruct.(compressed)...)]
	csize = sum(filesize.(compressed))

	diff = 0
	for (o, p) in zip(image, reconstructed)
		diff += colordiff(o, p)
	end

	(original_in_kb = original/1000, 
	comp_size_in_kb = csize/1000, 
	ratio = csize/original, 
	diff = diff)
end

# ╔═╡ 449a2e13-fe1f-49f8-a16d-7d160d396aa2
md"""
### Compression given a threshold
"""

# ╔═╡ 92c2398d-e393-48b3-a795-2a4afc799613
@bind threshold_color Slider(0.3:-0.001:0)

# ╔═╡ cb3e9ead-2e22-4b94-9ac2-8b63808df445
show_compressed(test, threshold_color)

# ╔═╡ 02839b7d-9944-4430-909a-cdba85cc64c2
compression_stats(test, threshold_color)

# ╔═╡ 703cf884-aa9a-4387-9a1b-afebdae5530e
md"Threshold is: $threshold_color"

# ╔═╡ 8ab423a8-4b33-477c-b445-1a10f86c260e
show_compressed(test, threshold_color)

# ╔═╡ 4b0750aa-70df-4bbe-8d90-fafea639f9af
md"""
### Average RGB
"""

# ╔═╡ c7404c7e-f847-4c27-be83-d8798a3c5dde
let
	c = mean([p for p in test])
	(r=c.r, g=c.g, b=c.b)
end

# ╔═╡ c3221ca6-7023-4bcc-865a-8c754ff45182
md"""
# Plotting! 
"""

# ╔═╡ dab7a6d7-a679-41f6-ab05-cf0a6cc5418c
plotly()

# ╔═╡ 220b0f16-4569-4187-a4e9-badf4dca946e
md"""
Collecting the data takes a good while (~20s)
"""

# ╔═╡ 8db87c95-64d6-4176-830a-c906c21125da
compression_stats(test, 0.3)

# ╔═╡ cc3a57d7-ee3b-4975-9973-bad0bb9f2f53
md"""
# Regression
"""

# ╔═╡ d3d3b840-70ef-4c4d-932f-0c259682d141
model(t, p) = p[1] * exp.(-p[2] * t)

# ╔═╡ c0e07072-6c6e-4ec5-9795-bc5d6bb74fe7
tdata = 0.3:-0.01:0

# ╔═╡ 01b82335-b1bd-457a-8bf8-9ec3de0bd375
test_data = [compression_stats(test, x) for x in tdata]

# ╔═╡ 0fc5c49f-2f2d-419e-a0cb-76a53b641fbe
let
	range = tdata
	canvas = plot(; xaxis="std threshold")
	plot!(range, [d.ratio for d in test_data], label="compression ratio")
	plot!(range, [1 / (log(100, d.diff + 1) + 1) for d in test_data], label="compression quality")
end

# ╔═╡ 4973ccbb-ea9b-49c3-b549-7b53c14dd685
begin
	fit1 = curve_fit(model, tdata, [d.ratio for d in test_data], [0.5, 0.5])
	p1 = fit1.param
	
	fit2 = curve_fit(model, tdata, [d.diff for d in test_data], [0.5, 0.5])
	p2 = fit2.param
	(ratio = p1, quality = p2)
end

# ╔═╡ 2b53da0c-c5dc-4788-9f28-36f5bb822559
plot(tdata, [model(t, p1) for t in tdata], label="ratio")

# ╔═╡ a772b2ce-5ef8-47a4-952b-683796fe3959
plot(tdata, [model(t, p2) for t in tdata], label="difference")

# ╔═╡ 133d23fa-d7d3-4dc8-b1f4-c8f068a8c07f
function camera_input(;max_size=500, default_url="https://i.imgur.com/SUmi94P.png")
"""
<span class="pl-image waiting-for-permission">
<style>
	
	.pl-image.popped-out {
		position: fixed;
		top: 0;
		right: 0;
		z-index: 5;
	}

	.pl-image #video-container {
		width: 250px;
	}

	.pl-image video {
		border-radius: 1rem 1rem 0 0;
	}
	.pl-image.waiting-for-permission #video-container {
		display: none;
	}
	.pl-image #prompt {
		display: none;
	}
	.pl-image.waiting-for-permission #prompt {
		width: 250px;
		height: 200px;
		display: grid;
		place-items: center;
		font-family: monospace;
		font-weight: bold;
		text-decoration: underline;
		cursor: pointer;
		border: 5px dashed rgba(0,0,0,.5);
	}

	.pl-image video {
		display: block;
	}
	.pl-image .bar {
		width: inherit;
		display: flex;
		z-index: 6;
	}
	.pl-image .bar#top {
		position: absolute;
		flex-direction: column;
	}
	
	.pl-image .bar#bottom {
		background: black;
		border-radius: 0 0 1rem 1rem;
	}
	.pl-image .bar button {
		flex: 0 0 auto;
		background: rgba(255,255,255,.8);
		border: none;
		width: 2rem;
		height: 2rem;
		border-radius: 100%;
		cursor: pointer;
		z-index: 7;
	}
	.pl-image .bar button#shutter {
		width: 3rem;
		height: 3rem;
		margin: -1.5rem auto .2rem auto;
	}

	.pl-image video.takepicture {
		animation: pictureflash 200ms linear;
	}

	@keyframes pictureflash {
		0% {
			filter: grayscale(1.0) contrast(2.0);
		}

		100% {
			filter: grayscale(0.0) contrast(1.0);
		}
	}
</style>

	<div id="video-container">
		<div id="top" class="bar">
			<button id="stop" title="Stop video">✖</button>
			<button id="pop-out" title="Pop out/pop in">⏏</button>
		</div>
		<video playsinline autoplay></video>
		<div id="bottom" class="bar">
		<button id="shutter" title="Click to take a picture">📷</button>
		</div>
	</div>
		
	<div id="prompt">
		<span>
		Enable webcam
		</span>
	</div>

<script>
	// based on https://github.com/fonsp/printi-static (by the same author)

	const span = currentScript.parentElement
	const video = span.querySelector("video")
	const popout = span.querySelector("button#pop-out")
	const stop = span.querySelector("button#stop")
	const shutter = span.querySelector("button#shutter")
	const prompt = span.querySelector(".pl-image #prompt")

	const maxsize = $(max_size)

	const send_source = (source, src_width, src_height) => {
		const scale = Math.min(1.0, maxsize / src_width, maxsize / src_height)

		const width = Math.floor(src_width * scale)
		const height = Math.floor(src_height * scale)

		const canvas = html`<canvas width=\${width} height=\${height}>`
		const ctx = canvas.getContext("2d")
		ctx.drawImage(source, 0, 0, width, height)

		span.value = {
			width: width,
			height: height,
			data: ctx.getImageData(0, 0, width, height).data,
		}
		span.dispatchEvent(new CustomEvent("input"))
	}
	
	const clear_camera = () => {
		window.stream.getTracks().forEach(s => s.stop());
		video.srcObject = null;

		span.classList.add("waiting-for-permission");
	}

	prompt.onclick = () => {
		navigator.mediaDevices.getUserMedia({
			audio: false,
			video: {
				facingMode: "environment",
			},
		}).then(function(stream) {

			stream.onend = console.log

			window.stream = stream
			video.srcObject = stream
			window.cameraConnected = true
			video.controls = false
			video.play()
			video.controls = false

			span.classList.remove("waiting-for-permission");

		}).catch(function(error) {
			console.log(error)
		});
	}
	stop.onclick = () => {
		clear_camera()
	}
	popout.onclick = () => {
		span.classList.toggle("popped-out")
	}

	shutter.onclick = () => {
		const cl = video.classList
		cl.remove("takepicture")
		void video.offsetHeight
		cl.add("takepicture")
		video.play()
		video.controls = false
		console.log(video)
		send_source(video, video.videoWidth, video.videoHeight)
	}
	
	
	document.addEventListener("visibilitychange", () => {
		if (document.visibilityState != "visible") {
			clear_camera()
		}
	})


	// Set a default image

	const img = html`<img crossOrigin="anonymous">`

	img.onload = () => {
	console.log("helloo")
		send_source(img, img.width, img.height)
	}
	img.src = "$(default_url)"
	console.log(img)
</script>
</span>
""" |> HTML
end

# ╔═╡ 5adf6861-9a4e-4347-8770-47df895038a6
function process_raw_camera_data(raw_camera_data)
	# the raw image data is a long byte array, we need to transform it into something
	# more "Julian" - something with more _structure_.
	
	# The encoding of the raw byte stream is:
	# every 4 bytes is a single pixel
	# every pixel has 4 values: Red, Green, Blue, Alpha
	# (we ignore alpha for this notebook)
	
	# So to get the red values for each pixel, we take every 4th value, starting at 
	# the 1st:
	reds_flat = UInt8.(raw_camera_data["data"][1:4:end])
	greens_flat = UInt8.(raw_camera_data["data"][2:4:end])
	blues_flat = UInt8.(raw_camera_data["data"][3:4:end])
	
	# but these are still 1-dimensional arrays, nicknamed 'flat' arrays
	# We will 'reshape' this into 2D arrays:
	
	width = raw_camera_data["width"]
	height = raw_camera_data["height"]
	
	# shuffle and flip to get it in the right shape
	reds = reshape(reds_flat, (width, height))' / 255.0
	greens = reshape(greens_flat, (width, height))' / 255.0
	blues = reshape(blues_flat, (width, height))' / 255.0
	
	# we have our 2D array for each color
	# Let's create a single 2D array, where each value contains the R, G and B value of 
	# that pixel
	
	return RGB.(reds, greens, blues)
end

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
FileIO = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
ImageIO = "82e4d734-157c-48bb-816b-45c225c6df19"
ImageShow = "4e3cecfd-b093-5904-9786-8bbb286a6a31"
LsqFit = "2fda8390-95c7-5789-9bda-21331edee243"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
QuartzImageIO = "dca85d43-d64c-5e67-8c65-017450d5d020"
Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

[compat]
Colors = "~0.12.8"
FileIO = "~1.12.0"
ImageIO = "~0.6.0"
ImageShow = "~0.3.3"
LsqFit = "~0.12.1"
Plots = "~1.25.8"
PlutoUI = "~0.7.34"
QuartzImageIO = "~0.7.4"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised

[[AbstractFFTs]]
deps = ["ChainRulesCore", "LinearAlgebra"]
git-tree-sha1 = "6f1d9bc1c08f9f4a8fa92e3ea3cb50153a1b40d4"
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[[AbstractPlutoDingetjes]]
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[[Adapt]]
deps = ["LinearAlgebra"]
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version = "3.3.3"

[[ArgTools]]
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version = "1.1.1"

[[ArrayInterface]]
deps = ["Compat", "IfElse", "LinearAlgebra", "Requires", "SparseArrays", "Static"]
git-tree-sha1 = "745233d77146ad221629590b6d82fe7f1ddb478f"
uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
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[[Artifacts]]
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[[Bzip2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "19a35467a82e236ff51bc17a3a44b69ef35185a2"
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[[CEnum]]
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version = "0.4.1"

[[Cairo]]
deps = ["Cairo_jll", "Colors", "Glib_jll", "Graphics", "Libdl", "Pango_jll"]
git-tree-sha1 = "d0b3f8b4ad16cb0a2988c6788646a5e6a17b6b1b"
uuid = "159f3aea-2a34-519c-b102-8c37f9878175"
version = "1.0.5"

[[Cairo_jll]]
deps = ["Artifacts", "Bzip2_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "4b859a208b2397a7a623a03449e4636bdb17bcf2"
uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
version = "1.16.1+1"

[[ChainRulesCore]]
deps = ["Compat", "LinearAlgebra", "SparseArrays"]
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[[ColorSchemes]]
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[[ColorVectorSpace]]
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[[Colors]]
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[[CommonSubexpressions]]
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[[DataStructures]]
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[[DensityInterface]]
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[[DiffRules]]
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[[Distributed]]
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[[Distributions]]
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[[DocStringExtensions]]
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[[EarCut_jll]]
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[[Expat_jll]]
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[[FFMPEG]]
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[[FFMPEG_jll]]
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[[FileIO]]
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[[FileWatching]]
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[[FixedPointNumbers]]
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[[Fontconfig_jll]]
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[[ForwardDiff]]
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[[FreeType2_jll]]
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[[FriBidi_jll]]
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[[GLFW_jll]]
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[[GR]]
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[[GR_jll]]
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[[GeometryBasics]]
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[[Gettext_jll]]
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[[Glib_jll]]
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[[Graphics]]
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[[Graphite2_jll]]
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[[Grisu]]
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[[HTTP]]
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[[HarfBuzz_jll]]
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[[Hyperscript]]
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[[HypertextLiteral]]
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[[IOCapture]]
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[[IfElse]]
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[[ImageCore]]
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[[ImageIO]]
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[[ImageShow]]
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[[Imath_jll]]
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[[IndirectArrays]]
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[[Inflate]]
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[[IniFile]]
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[[InteractiveUtils]]
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[[InverseFunctions]]
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[[IrrationalConstants]]
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[[IteratorInterfaceExtensions]]
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[[JLLWrappers]]
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[[JSON]]
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[[JpegTurbo_jll]]
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[[Juno]]
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[[LAME_jll]]
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[[LZO_jll]]
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[[LaTeXStrings]]
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[[Latexify]]
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[[LibCURL]]
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[[LibCURL_jll]]
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[[LibGit2]]
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[[LibSSH2_jll]]
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[[Libdl]]
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[[Libffi_jll]]
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[[Libgcrypt_jll]]
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[[Libglvnd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"]
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[[Libgpg_error_jll]]
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uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
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[[Libiconv_jll]]
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git-tree-sha1 = "42b62845d70a619f063a7da093d995ec8e15e778"
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[[Libmount_jll]]
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[[Librsvg_jll]]
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[[Libtiff_jll]]
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uuid = "89763e89-9b03-5906-acba-b20f662cd828"
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[[Libuuid_jll]]
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[[LinearAlgebra]]
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[[LogExpFunctions]]
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[[Logging]]
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[[LsqFit]]
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[[Luxor]]
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[[MacroTools]]
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[[MbedTLS]]
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[[MbedTLS_jll]]
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[[Measures]]
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[[Media]]
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[[Missings]]
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[[Mmap]]
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[[MosaicViews]]
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[[MozillaCACerts_jll]]
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version = "2020.7.22"

[[NLSolversBase]]
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[[NaNMath]]
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[[Netpbm]]
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[[NetworkOptions]]
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[[OffsetArrays]]
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[[Ogg_jll]]
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[[OpenBLAS_jll]]
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[[OpenEXR]]
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[[OpenEXR_jll]]
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[[OpenLibm_jll]]
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[[OpenSSL_jll]]
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[[OpenSpecFun_jll]]
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[[OptimBase]]
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[[Opus_jll]]
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[[OrderedCollections]]
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[[PCRE_jll]]
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[[PDMats]]
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[[PNGFiles]]
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[[Parsers]]
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[[Pixman_jll]]
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[[PkgVersion]]
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[[PlotUtils]]
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[[Plots]]
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[[PlutoUI]]
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[[Preferences]]
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[[Printf]]
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[[Profile]]
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[[ProgressMeter]]
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[[QOI]]
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[[Qt5Base_jll]]
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[[QuadGK]]
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[[QuartzImageIO]]
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[[REPL]]
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[[Random]]
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[[RecipesBase]]
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[[RecipesPipeline]]
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[[RelocatableFolders]]
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[[Requires]]
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[[Rmath]]
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[[Rmath_jll]]
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[[Rsvg]]
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[[SHA]]
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[[Scratch]]
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[[Serialization]]
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[[Showoff]]
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[[Sixel]]
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[[Sockets]]
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[[SortingAlgorithms]]
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[[SparseArrays]]
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[[SpecialFunctions]]
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[[StackViews]]
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[[Static]]
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[[StaticArrays]]
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[[Statistics]]
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[[StatsBase]]
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version = "0.33.14"

[[StatsFuns]]
deps = ["ChainRulesCore", "InverseFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
git-tree-sha1 = "f35e1879a71cca95f4826a14cdbf0b9e253ed918"
uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
version = "0.9.15"

[[StructArrays]]
deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
git-tree-sha1 = "d21f2c564b21a202f4677c0fba5b5ee431058544"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
version = "0.6.4"

[[SuiteSparse]]
deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]
uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"

[[TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
version = "1.0.0"

[[TableTraits]]
deps = ["IteratorInterfaceExtensions"]
git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
version = "1.0.1"

[[Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
git-tree-sha1 = "bb1064c9a84c52e277f1096cf41434b675cd368b"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.6.1"

[[Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
version = "1.10.0"

[[TensorCore]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
version = "0.1.1"

[[Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[[TiffImages]]
deps = ["ColorTypes", "DataStructures", "DocStringExtensions", "FileIO", "FixedPointNumbers", "IndirectArrays", "Inflate", "OffsetArrays", "PkgVersion", "ProgressMeter", "UUIDs"]
git-tree-sha1 = "991d34bbff0d9125d93ba15887d6594e8e84b305"
uuid = "731e570b-9d59-4bfa-96dc-6df516fadf69"
version = "0.5.3"

[[URIs]]
git-tree-sha1 = "97bbe755a53fe859669cd907f2d96aee8d2c1355"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.3.0"

[[UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
version = "0.4.1"

[[Unzip]]
git-tree-sha1 = "34db80951901073501137bdbc3d5a8e7bbd06670"
uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
version = "0.1.2"

[[Wayland_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "3e61f0b86f90dacb0bc0e73a0c5a83f6a8636e23"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.19.0+0"

[[Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "66d72dc6fcc86352f01676e8f0f698562e60510f"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.23.0+0"

[[XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "1acf5bdf07aa0907e0a37d3718bb88d4b687b74a"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.9.12+0"

[[XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.34+0"

[[Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.6.9+4"

[[Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.9+4"

[[Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.0+4"

[[Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.3+4"

[[Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.4+4"

[[Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "5.0.3+4"

[[Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"

[[Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"

[[Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"

[[Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"

[[Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"

[[Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"

[[Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.0+4"

[[Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"

[[Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"

[[Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"

[[Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"

[[Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.2+4"

[[Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.27.0+4"

[[Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"

[[Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.12+1"

[[Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e45044cd873ded54b6a5bac0eb5c971392cf1927"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.2+0"

[[gdk_pixbuf_jll]]
deps = ["Artifacts", "Glib_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pkg", "Xorg_libX11_jll", "libpng_jll"]
git-tree-sha1 = "c23323cd30d60941f8c68419a70905d9bdd92808"
uuid = "da03df04-f53b-5353-a52f-6a8b0620ced0"
version = "2.42.6+1"

[[libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[libblastrampoline_jll]]
deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.0.1+0"

[[libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[libsixel_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "78736dab31ae7a53540a6b752efc61f77b304c5b"
uuid = "075b6546-f08a-558a-be8f-8157d0f608a5"
version = "1.8.6+1"

[[libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"

[[nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.41.0+1"

[[p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "16.2.1+1"

[[x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "0.9.1+5"
"""

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